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Plasma Flow Numerical Investigations


Plasma Flow Numerical Investigations via Basic Two-Fluid Model: Accurate and Efficient Discretization on Unstructured Grid

Tech Area / Field

  • INF-COM/High Performance Computing and Networking/Information and Communications
  • INF-SOF/Software/Information and Communications
  • PHY-NGD/Fluid Mechanics and Gas Dynamics/Physics

8 Project completed

Registration date

Completion date

Senior Project Manager
Komarkov D A

Leading Institute
Neurok Techsoft Ltd, Russia, Moscow


  • CNRS / Ecole Polytechnique / Laboratore de Physique et Technologie des Plasmas, France, Palaiseau

Project summary

Mathematical models of magneto-hydrodynamic are a universal way for investigation of a low frequencies plasma phenomena, i.e. in the frequency band below the ion-cyclotron frequency WCi. The ionic and electronic components of plasma uniformly respond to external fields in the low frequency range of flows in ideal media that is expressed in identical drift velocity of particles cExB/B2. The basic frequencies are determined by ionic inertia and forces maintaining constancy of a magnetic flow captured by plasma (freezing-in condition).

The analysis in the range of higher frequencies causes accounting of persity of average (macroscopic) speeds of ions and electrons. As it is known, wave dispersion becomes essential in the frequencies range about WCi and higher and plasma shows gyrotropic properties. For such theory there exist numerous applications. As an example can be served a situation experimentally observed in a plasma focus, when the Larmor radius of ions RLi appears comparable with flow region size L, while the RLe<<L condition is valid for electrons, could be taken. Ions slip across the magnetic field, while electrons move along magnetic field lines compensating quasineutrality perturbation and smoothing the electrical potential. Thus, electrons and ions can not drift any more with identical speed, it is necessary to proceed to the description of plasma based on two-liquid model.

The model of two liquids which is not taking into account inertia of electrons (model with Hall effect) is widely known. In such model frequencies are limited from above by WCi. Its area of applicability is rather narrow and correct computational algorithm construction represents a difficult task for this model. At the same time many practically important plasma processes occur in higher frequencies - in range from WCi up to WCe.

The most full consistent account of the listed phenomena can be done within the framework of two-liquid model directly following from the kinetic description of plasma components. Let's give the brief description of this approach following ideas from the well-known paper of S.I.Braginskiy (Phenomena of transfer in plasma, VTP, vol. 1, 1967).

There is a wide area of plasma phenomena, which is boundary between dense and completely collisionless plasma. The research of various sausage-type plasma instabilities, plasma coronas of the self-constrained discharges, configurations of mentioned above plasma focus type and many others are actual here. At last we should note, that the model implementation could be done to take into consideration derivation of ion distribution function from equilibrium (large track, large larmor radius of ions), i.e. on the basic of macro-particles method. The reversed situation is possible, when following the excitation (electromagnetic wave pumping) of electronic components in dense, but not completely ionized plasma, the deviation from LTR occurs only for the electronic distribution function, but ionic component has locally Maxwell form due to large frequency of collisions with neutrals. There is an application area of various microwave discharges in a low-temperature plasma.

Thus, the numerical analysis of the full two-liquid model would allow obtaining new interesting physical results. Therefore the construction of an effective method of an approximate solution is the important problem.

Finite-difference methods, macroscopic particles methods and also every possible their combinations in the 3-dimensional approach are proposed to be used in the presented project for creation of the numerical algorithms for the two-liquid MHD equations. The approximations will be implemented on non-structured triangular grids forming the system of Voronoi cells. The code will be developed in the frame of the object-oriented approach.